I've been studying this idea a bit further, and think there is a fallacy in this reasoning, that is, you are giving the author his present value at publication, but you are not giving it at the present, but spread out of N years.... Under your assumptions, he can consume A forever from day zero with perpeptual copyright, but he will have to wait for N years (and save everything, except interest) before he can consume A forever after this deal. Since most people don't life forever, this isn't a very good deal. I think you can still make a good economical case for a copyright lasting in the order of 28 years, but that will require some more math, and statistics about sales patterns of common copyrighted works. That's why I wanted to throw in the VAT, or even some arbitrary valuation of elements borrowed from the public domain, so that we can claim a work for the public when the author has earned roughly 85 % of its value according to very conservative estimates. Jeroen Hellingman. Robert Shimmin wrote:
The sad truth is that when approached from an economic point of view, the optimal length is so short that it seems absurd, and nobody takes you seriously after they hear the result. Here's the analysis:
Let's say that we have a work of enduring reputation, so that the right to publish it is worth a perpetuity of some annual income A. The copyright then has a present value of A/r, where r is the interest rate. We wish to transfer the copyright from the rights holder to the public when the public has paid the rights holder A/r.
The public pays the rights holder A per year, and if this money accrues interest at the same rate r, then (omitting a pile of algebra), then the public will have paid the rights holder A/r after N years, where N=log(2)/log(1+r). Those with some accounting knowledge will recognize that the optimal copyright term at some interest rate is the same time as the doubling time of money at that interest rate:
interest copyright rate term 2% 35.0 yr 3% 23.4 yr 4% 17.7 yr 5% 14.2 yr 6% 11.9 yr 7% 10.2 yr
It's interesting to note that the copyright term of the legislation that started the Anglo-American copyright tradition, the 1710 Statue of Anne, hit this range on the nose with a 14 year term (5% interest). It got the number from the 1624 Statute of Monopolies, which limited royal monopolies to 14 years. In patent law, where the economic disadvantages of too long a patent term are quite clear, most patent offices have kept patent terms in the 14-20 year range, which seems reasonable, looking at the table above. In copyright law, the Continental jurists won the day, and things have gotten out of hand ever since.